Details

sample61.0ms

Algorithm

intervals

Results

20.0ms	42×	body	1280	valid
20.0ms	52×	body	640	valid
8.0ms	140×	body	80	valid
3.0ms	15×	body	320	valid
1.0ms	7×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	9
1	43	9
2	93	9
3	174	9
4	269	9
5	288	9
6	288	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))
16.6b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-cbrt-cube`
19×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
13×	`times-frac`
12×	`prod-exp` `cbrt-unprod`
10×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`associate-r`
5×	`associate-*l/`
4×	`pow-prod-down`
3×	`associate-/r*` `add-log-exp`
2×	`*-commutative` `div-inv` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/l/` `associate-/l*`

Counts

3 → 79

Calls

3 calls:

20.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
10.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
19.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series172.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
42.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
78.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify55.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	402	818
1	2097	614
2	5002	599

prune221.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
0.2b	(/ (sin (* 0.5 x)) (sin x))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
28×	`times-frac`
26×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-r`
14×	`associate-l`
12×	`prod-exp` `cbrt-unprod`
10×	`pow1`
7×	`cbrt-undiv` `div-exp`
4×	`pow-prod-down` `associate-*l/`
3×	`associate-/r` `div-inv` `associate-/l` `add-log-exp`
2×	`*-commutative` `unswap-sqr`
1×	`frac-times` `frac-2neg` `associate-*r/` `clear-num`

Counts

3 → 98

Calls

3 calls:

25.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
4.0ms	(/ (sin (* 0.5 x)) (sin x))
10.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series154.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
44.0ms	(/ (sin (* 0.5 x)) (sin x))
37.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify68.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	463	970
1	2477	779
2	5002	764

prune261.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* 8.0 (sin (* x 0.5))) 3.0)
0.2b	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* 0.5 x)) (sin x)))
0.2b	(/ (sin (* 0.5 x)) (sin x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-cbrt-cube`
27×	`add-sqr-sqrt`
25×	`times-frac`
22×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-l`
6×	`associate-/r*`
5×	`pow1`
4×	`div-inv` `associate-/l*`
3×	`add-log-exp`
2×	`frac-2neg` `clear-num` `unswap-sqr`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

3 → 94

Calls

3 calls:

5.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
15.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* 0.5 x)) (sin x)))
4.0ms	(/ (sin (* 0.5 x)) (sin x))

series154.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
78.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* 0.5 x)) (sin x)))
42.0ms	(/ (sin (* 0.5 x)) (sin x))

simplify60.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	458	994
1	2410	812
2	5001	788

prune452.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (/ 3.0 (* 8.0 (sin (* x 0.5))))) (/ (sin (* 0.5 x)) (sin x)))
0.2b	(/ (sin (* 0.5 x)) (sin x))
0.2b	(/ 3.0 (* 8.0 (sin (* x 0.5))))
0.3b	(/ 1 (/ 3.0 (* 8.0 (sin (* x 0.5)))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

106×	`add-exp-log`
91×	`times-frac`
68×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
52×	`add-cbrt-cube`
51×	`add-cube-cbrt`
49×	`div-exp`
30×	`prod-exp`
26×	`associate-l`
22×	`cbrt-undiv`
13×	`associate-r`
12×	`cbrt-unprod` `div-inv`
11×	`associate-/r*`
9×	`rec-exp` `1-exp` `associate-/l*`
7×	`pow1`
6×	`unswap-sqr`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`associate-/r/`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 189

Calls

4 calls:

38.0ms	(* (/ 1 (/ 3.0 (* 8.0 (sin (* x 0.5))))) (/ (sin (* 0.5 x)) (sin x)))
4.0ms	(/ (sin (* 0.5 x)) (sin x))
4.0ms	(/ 3.0 (* 8.0 (sin (* x 0.5))))
9.0ms	(/ 1 (/ 3.0 (* 8.0 (sin (* x 0.5)))))

series187.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (/ 1 (/ 3.0 (* 8.0 (sin (* x 0.5))))) (/ (sin (* 0.5 x)) (sin x)))
37.0ms	(/ (sin (* 0.5 x)) (sin x))
38.0ms	(/ 3.0 (* 8.0 (sin (* x 0.5))))
35.0ms	(/ 1 (/ 3.0 (* 8.0 (sin (* x 0.5)))))

simplify100.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	795	2013
1	3987	1688
2	5001	1606

prune409.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0b

regimes40.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	9
1	17	9
2	17	9

end0.0ms

sample1.7s

Algorithm

intervals

Results

722.0ms	1513×	body	1280	valid
380.0ms	1231×	body	640	valid
280.0ms	4339×	body	80	valid
130.0ms	622×	body	320	valid
41.0ms	295×	body	160	valid